The unequal step time cycle studied comprise of three beds each of which undergoes eight different cycle steps including one pressure equalization step, as shown in Figure 2.1. Details of each of these cycle steps are given below:
Step-1: Feed (240 s): The first step of the cycle is the Feed step (F) where a binary gas mixture of 74.09 % CH4 and 25.91 % CO2 entering the bed at high pressure. The Heavy Gas (i.e. CO2), either more adsorbable for 13X or fast adsorbing on CMS, gets preferentially adsorbed in the column while light gas (i.e. CH4) leaves through the top of the bed accepted as Light Product.
Step-2: Equalization-Down (40 s): The second step is the pressure equalization step (E). There is no inlet stream at these step. Exit stream is decreasing the bed pressure by providing the gas from light end of the bed into the light end of EQUALIZATION-UP step until pressures of beds undergoing equalization down and up steps are equal.
Step-3: Co-Current Depressurization (40 s): The third step is the co-current depressurization step during which the gas leaving the bed from light end until an intermediate pressure achieved right before counter-current depressurization step (which undergoes at vacuum pressures). There is no inlet stream at this step. Exit stream is going through a compressor then into Light End Pressurization step.
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Step-4: Counter-Current Depressurization (120 s): The fourth step is the counter-current depressurization step during which there is no inlet stream. Exit stream leaving the bed from Heavy End of the bed (z/L=0) by a vacuum pump and is accepted as Heavy Product. This step is also called as Blow-Down step in which bed pressure is significantly going down by the help of Vacuum pumps. It is a significant step for regeneration of the adsorbent. Gas flow is in the reverse direction (Counter current) of Feed step.
Step-5: Light Reflux (40 s): The fifth step is the Light Reflux step during which a fraction of light product (which is known as Light Reflux Ratio) flow into this step from light end (z/L=1) at low pressure. Exit stream is also accepted as Heavy Product. The bed is still under vacuum at this step. It is another significant step for regeneration of the adsorbent by purging with a slight portion of Light Product. The fraction of the Light Product feeding this step is fixed as 5 % of Light Product. Gas flow is in the reverse direction (Counter current) of Feed step.
Step-6: Equalization-Up (40 s): The sixth step is Equalization-Up step during which there is no exit stream. Inlet stream is the gas coming from Equalization-Down step and equalizing the bed pressures with Equalization-Down step (#2). Bed pressure is going up on this step.
Step-7: Light End Pressurization (40 s): The seventh step is Light End Pressurization step during which there is no exit stream. The compressed gas coming from CoD step (#3) provides to this step from light end (z/L=1) as a first pressurization of the bed. Bed pressure is going up again. Gas flow is in the reverse direction of the Feed step.
Step-8: Light Product Pressurization (160 s): Finally, during the eighth and final step, the bed receives a fraction of the light product gas exiting the bed undergoing the Feed step
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into the light product end (z/L=1) in a counter-current direction till the pressure rises to feed pressure, which is the highest pressure in the cycle. This step is termed as the Light Product Pressurization step (LPP). There is no exit stream at this step.
2.6 Results and Discussion
Binary gas mixture of 74.09 % CH4 and 25.91 % CO2 was fed into the three bed eight step PSA system at 790.5 kPa and 305.15 K. The performance target is to achieve above 97 % CH4 purity and 90 % CH4 recovery in the light product by maximizing feed throughput (L STP L-1h-1). The feed throughput was used in this study was chosen per volume of the bed on purpose, since the study reveals the effect of different layer combinations of adsorbents with different pellet densities. As mentioned earlier the effect of different model approaches of mixed gas adsorption isotherms on the separation performance was also investigated by mainly applying either perfect negative or perfect positive approaches for Carbon Molecular Sieve and 13X adsorbents.
The results shown in three main parts as: 1) the effect of layer combinations for Perfect Negative binary gas isotherm approach applied on both CMS and 13X, 2) the effect of layer combinations for Perfect Negative binary gas isotherm approach applied on CMS and Perfect Positive binary gas isotherm approach applied on 13X, 3) Perfect Positive binary gas isotherm approach applied on both CMS and 13X adsorbents. On each separate part, the effect of feed throughput is also investigated and energy required for the particular separation was given in separate graphs.
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1) Effect of Layer Combinations if PN approach applied on both adsorbents: In order to investigate the effect of amount of CMS in front of 13X adsorbent in the bed, 6 set of simulations done. Each set of simulations, in particular, has the simulations of 6 different feed throughputs (total of 36 simulations). The performances of simulations are given as % CH4 recovery and purity in Light Product (see Figure 2.2 and Table 2.5) and % CO2 recovery and purity in Heavy Product (see Figure 2.3 and Table 2.5). It can be seen from Figure 2.2 that as feed throughput increases the % CH4 recovery also increases while % CH4 purity decreases. This behavior can be easily explained by checking the gas loading profiles of different feed throughputs at the end of feed step (see Figure 2.11). It can be easily seen from Figure 2.11a that more CO2, heavy product, is breaking through the column as feed throughput increased, which results less recoverable CO2 in the bed. Namely, more CO2 suppresses the CH4 in the bed as it approaches to the light end of the column. As methane loadings suppressed it leads more methane to leave the bed in gas form and that results an increase in the CH4 recoveries. However, the increase on the CO2, heavy product, loadings results also more CO2 to leave the bed at feed step which leads a decrease of the purity of CH4 in Light Product.
On the other hand, better performances can be achieved as CMS amount in the layers increased from 0 % to 100 % for PN-PN mixed gas isotherms approach. This result, by itself, teaches that the PN approach cannot be true for 13X adsorbent on the separation of CO2-CH4, since it is well known fact that 13X filled beds are good candidates on the separation of CO2-CH4. Hence, PN approach for 13X adsorbent is not used for the further simulations.
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2) Effect of Layer Combinations if PN-PP approach applied on CMS and 13X, respectively:
In order to investigate the effect of amount of CMS in front of 13X adsorbent in the bed, 5 new set of simulations done. Each set of simulations, in particular, has the simulations of 6 different feed throughputs (total of 30 new simulations). The performances of simulations are given as % CH4 recovery and purity in Light Product (see Figure 2.5 and Table 2.6) and % CO2 recovery and purity in Heavy Product (see Figure 2.6 and Table 2.6). It can be seen from Figure 2.5 that as feed throughput increases the % CH4 recovery also increases while % CH4 purity decreases. On the other hand, slightly better performances can be achieved as CMS amount in the layers decreased from 100 % to 0 % for PN-PP mixed gas isotherms approach. This is totally different than what has been shown in PN- PN approach and further investigated in details experimentally in another study of authors (Erden, Ebner, and Ritter 2016e; Erden, Ebner, and Ritter 2016f; Erden, Ebner, and Ritter 2016d).
3) Effect of Layer Combinations if PP approach applied on both adsorbents: The effect of CMS amount in front of 13X adsorbent in the bed was investigated by running 5 new set of simulations. Each set of simulations, in particular, has the simulations of 6 different feed throughputs (total of 30 new simulations). The performances of simulations are given as % CH4 recovery and purity in Light Product (see Figure 2.8 and Table 2.7) and % CO2 recovery and purity in Heavy Product (see Figure 2.9 and Table 2.7). It can be seen from Figure 2.8 that as feed throughput increases the % CH4 recovery also increases while % CH4 purity decreases. On the other hand, better performances can be achieved as CMS amount in the layers decreased from 100 % to 0 % for PN-PP mixed gas
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isotherms approach. This results showed that 13X adsorbent was shown better performance on this PSA cycle for purification of CH4 out of CO2.
The required energy for the separation of CH4 out of CO2 via this particular PSA cycle was given for PN-PN, PN-PP, and PP-PP approaches in Figures 2.4, 2.7, 2.10, respectively. Energy is consumed cumulatively during the CnD and the LR steps by means of vacuum pump at the end, additionally the exit stream of CoD step is pressurized to an intermediate pressure and used in Light End Pressurization step. The combination of energies required in all three steps were used as final energy requirement per moles of CH4 produced in units of kJ.(moles of CH4 produced)-1. It can be easily seen that required energy is a strong function of process performance, since the energy requirements are decreased as better performances achieved. It is mainly because the amount of gas processed are smaller if higher CH4 purities are achieved, which directly relates with compressor work.
2.7 Conclusion
A Pressure Swing Adsorption (PSA) process was described that is capable of handling 74.09 % CH4 and 25.91 % CO2 binary gas mixture for separating CH4 to pipeline quality (>97 % CH4) with high recoveries (>90 % CH4). Layered bed of Carbon Molecular Sieve and 13X was used as adsorbents by varying the amount of CMS from 0 to 100 % in the beds. The effect of feed throughputs were investigated for three different mixed gas adsorption isotherm approaches as Perfect Negative for both adsorbents, Perfect Negative for CMS and Perfect Positive for 13X, and Perfect Positive approach for both adsorbents. The results obviously showed that Perfect Negative approach is not true for 13X, since it is a well-known fact that 13X filled beds are in use of CO2-CH4 separation already.
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However it is still a mystery that if PN or PP is valid for CMS material used in this study, since they showed slight differences on performances.
The feed throughput was found to significantly affect process performance. As feed throughput increased by increasing total feed flowrate, % CH4 recoveries increased while % CH4 purities decreased in Light Product, and also % CO2 recoveries decreased and % CO2 purities increased in Heavy Product, contrarily. The higher % recoveries of CH4 in Light Product is attributed to the CO2 front in the bed moved further in the bed as feed throughputs increased, which also causes a decrease on % CH4 purities.
Overall this study shows that the pipeline quality Methane with more than 90 % recoveries can be achieved by 3 bed 8 step PSA cycle via both CMS and 13X adsorbents. The performance of PSA cycle also revealed that Perfect Negative mixed adsorption isotherm approach cannot be true for 13X but further experimental study is required to validate which mixed adsorption isotherm to be used in either CMS or 13X adsorbents. 13X filled beds shown the best % CH4 recoveries and purities with less energy requirements.
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Table 2.1 TPL Fitting parameters for CO2 and CH4 on CMS adsorbent.
CO2-CMS CH4-CMS
site-1 site-2 site-3 site-1 site-2 site-3
𝒒𝒊𝒔 0.6811 2.5366 1.3336 1.0492 1.9502 1.3231
𝒃𝒊𝒐 1.922E-07 3.683E-07 2.703E-09 2.649E-07 8.656E-07 2.630E-09
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Table 2.2 TPL Fitting parameters for CO2 and CH4 on 13X adsorbent.
CO2-13X CH4-13X
site-1 site-2 site-3 site-1 site-2 site-3
𝒒𝒊𝒔 1.3794 2.9629 1.6194 4.1259 0.0000 0.0000
𝒃𝒊𝒐 2.716E-08 4.302E-08 1.021E-08 5.820E-07 0.000E+00 0.000E+00
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Table 2.3 PSA bed properties, process characteristics, adsorbent properties, and kinetic properties. Bed Characteristics Bed radius (m) 0.0254 Bed length (m) 0.508 Bed porosity 0.40 Bulk density (kg/m3) [CMS, 13X] 1060, 1180
Heat of adsorption (kJ/mol) CH4, CO2 [CMS, 13X] 23.14, 19.81, 27.16, 40.5
Heat transfer coefficient (kW/m2/K) 0.0
Adsorbent characteristics
Adsorbent CMS, 13X
Pellet radius (m) 0.0015
Pellet porosity 0.50
Pellet heat capacity (J/kg/K) [CMS, 13X] 0.8, 1.1
Process characteristics
Feed Throughput L(STP) L-1h-1 116.55 – 310.79
Cycle time (s) 720
Feed mole fraction: CH4, CO2 0.7409, 0.2591
Feed temperature (K) 305.15
High pressure (kPa) 790.5
Low pressure (kPa) 15.0
Kinetic information
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Table 2.4 Initial conditions, boundary conditions and balances for the PSA cycle.
Step Time & bed
location Initial conditions, boundary conditions and balances
F
t = 0, 0 < z/L < 1 yi, F = yi,LPP, f, vF = vLPP, f, qi, F = qi,LPP, f, TF = TLPP, f, PF = PLPP, f
z/L = 0, t ≥ 0 yi, F =
y
Fi, T = TF, F = FF, L.D.F.E.(i=1,m), M.B.z/L = 1, t ≥ 0 C.M.B.(i=1,m), O.M.B., L.D.F.E.(i=1,m), E.B., V.E.(Po = PH, cv>0)
Eq
t = 0, 0 < z/L < 1 yi,Eq = yi,F,f, vEq = vF, f, qi, Eq = qi,F, f, TEq = TF,f, PEq = PF,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B., M.B., V.E.(Po =PEq, cv = 0)
z/L = 1, t ≥ 0 C.M.B.(i=1,m), O.M.B., L.D.F.E.(i=1,m), E.B., V.E.(Po =PEq, cv > 0)
CoD
t = 0, 0 < z/L < 1 yi,CoD = yi,Eq,f, vCoD = vEq, f, qi, CoD = qi,Eq, f, TCoD = TEq,f, PCoD = PEq,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B., V.E.(Po =PCoD, cv = 0), M.B.
z/L = 1, t ≥ 0 C.M.B.(i=1,m), O.M.B., L.D.F.E.(i=1,m), E.B., V.E.(Po = PCoD, cv > 0)
CnD
t = 0, 0 < z/L < 1 yi,CnD = yi,CoD,f, vCnD = vCoD, f, qi, CnD = qi,CoD, f, TCnD = TCoD,f, PCnD = PCoD,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), O.M.B., L.D.F.E.(i=1,m), E.B., V.E.(Po = PL, cv > 0)
z/L = 1, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B., V.E.(Po =PL, cv = 0)
LR
t = 0, 0 < z/L < 1 yi,LR = yi,CnD,f, vLR = vCnD, f, qi, LR = qi,CnD, f, TLR = TCnD,f, PLR = PCnD,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B.
z/L = 1, t ≥ 0 yi,LR = yi,F,z/L=1, FLR = -LRR*FF,z/L=1, L.D.F.E.(i=1,m), M.B.
Eq*
t = 0, 0 < z/L < 1 yi,Eq* = yi,LR,f, vEq* = vLR, f, qi, Eq* = qi,LR, f, TEq* = TLR,f, PEq* = PLR,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B., M.B., V.E.(Po =PEq, cv = 0)
z/L = 1, t ≥ 0 yi,Eq* = yi,Eq,z/L=1, FEq* = -F Eq,z/L=1, L.D.F.E.(i=1,m), T = TFz/L=1, M.B.
LEP
t = 0, 0 < z/L < 1 yi,LEP = yi,Eq*,f, vLEP = vEq*, f, qi, LEP = qi,Eq*, f, TLEP = TEq*,f, PLEP = PEq*,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B., M.B, V.E.(Po =PL, cv = 0)
z/L = 1, t ≥ 0 yi,LEP = yi,CoD,z/L=1, FLEP = - FCoD,z/L=1, L.D.F.E.(i=1,m), TLEP = TCoD,z/L=1, M.B.
LPP
t = 0, 0 < z/L < 1 yi,LPP = yi,LEP,f, vLPP = vLEP, f, qi, LPP = qi,LEP, f, TLPP = TLEP,f, PLPP = PLEP,f
z/L = 0, t ≥ 0 C.M.B.(i=1,m), L.D.F.E.(i=1,m), E.B., M.B, V.E.(Po =PL, cv = 0)
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Table 2.5 Simulation results of layered bed PSA for adiabatic system; @ t=0; CO2: 25.91%, CH4: 74.09%. (PN-PN mixed isotherm)
1st layer
2nd layer
Feed Throughput HEAVY END LIGHT END
Rec. % Pur. % Rec. % Pur. %
CMS 13X L(STP) L-1h-1 CO 2 CO2 CH4 CH4 0 100 116.55 81.22 35.06 47.39 87.83 155.40 61.10 35.45 61.09 81.79 194.24 49.10 35.55 68.85 79.46 233.09 41.12 35.59 73.99 78.23 271.94 35.44 35.63 77.61 77.46 310.79 31.19 35.66 80.32 76.95 20 80 116.55 100.67 35.12 35.24 99.94 155.40 83.40 47.17 67.36 92.07 194.24 66.73 48.10 74.82 86.55 233.09 55.67 48.28 79.15 83.62 271.94 47.82 48.30 82.11 81.81 310.79 41.97 48.30 84.28 80.59 40 60 116.55 97.92 44.43 57.95 99.86 155.40 99.85 56.14 72.77 99.92 194.24 84.95 61.47 81.40 93.95 233.09 70.56 62.15 84.94 89.21 271.94 60.46 62.01 87.05 86.30 310.79 52.91 61.82 88.56 84.33 60 40 116.55 100.00 52.73 70.07 99.90 155.40 98.33 59.97 77.67 99.93 194.24 96.09 70.19 85.73 98.46 233.09 82.65 74.42 90.07 93.71 271.94 70.79 74.79 91.64 89.99 310.79 62.00 74.49 92.57 87.45 80 20 116.55 98.35 65.64 82.56 99.96 155.40 99.89 72.82 86.95 99.98 194.24 99.67 77.26 89.89 99.99 233.09 89.86 84.44 94.26 96.38 271.94 77.54 85.91 95.58 92.42 310.79 68.08 85.65 95.99 89.58 100 0 116.55 99.98 88.06 95.34 100.00 155.40 99.62 91.09 96.51 99.86 194.24 98.76 92.97 97.53 99.56 233.09 93.19 93.84 97.98 97.63 271.94 80.96 93.56 98.08 93.64 310.79 71.50 93.30 98.22 90.78
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Table 2.6 Simulation results of layered bed PSA for adiabatic system; @ t=0; CO2: 25.91%, CH4: 74.09%. (PN for CMS, PP for 13X mixed isotherm)
1st layer 2nd layer Feed Throughput
HEAVY END LIGHT END
Rec. % Pur. % Rec. % Pur. %
CMS 13X L(STP) L-1h-1 CO 2 CO2 CH4 CH4 0 100 116.55 96.13 89.07 96.11 98.75 155.40 99.75 90.31 96.17 99.72 194.24 98.75 94.72 98.05 99.46 233.09 97.84 96.56 98.70 99.18 271.94 91.55 97.09 99.00 97.01 310.79 78.92 96.62 99.05 93.07 20 80 116.55 98.90 51.42 67.81 99.93 155.40 99.23 68.46 84.39 99.96 194.24 98.59 94.93 98.21 99.50 233.09 93.49 95.97 98.60 97.82 271.94 78.84 95.58 98.73 93.07 310.79 68.36 95.28 98.87 89.95 40 60 116.55 98.43 45.33 59.02 99.97 155.40 99.83 53.69 70.02 99.99 194.24 99.48 91.52 96.84 99.81 233.09 98.53 95.39 98.37 99.48 271.94 87.40 95.21 98.52 95.76 310.79 75.32 94.79 98.54 91.96 60 40 116.55 99.78 53.48 69.71 100.00 155.40 99.83 54.97 71.48 100.00 194.24 99.35 91.44 96.80 99.77 233.09 96.36 94.68 98.11 98.77 271.94 84.82 94.67 98.40 94.94 310.79 73.32 94.33 98.47 91.36 80 20 116.55 98.70 65.97 82.74 100.00 155.40 99.58 72.78 87.15 100.00 194.24 99.37 92.15 96.94 99.77 233.09 96.56 94.37 97.97 98.84 271.94 82.46 93.99 98.09 94.14 310.79 72.02 93.70 98.34 90.97 100 0 116.55 99.98 88.06 95.34 100.00 155.40 99.62 91.09 96.51 99.86 194.24 98.76 92.97 97.53 99.56 233.09 93.19 93.84 97.98 97.63 271.94 80.96 93.56 98.08 93.64 310.79 71.50 93.30 98.22 90.78
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Table 2.7 Simulation results of layered bed PSA for adiabatic system; @ t=0; CO2: 25.91%, CH4: 74.09%. (PP-PP mixed isotherm) 1st layer 2nd layer Feed Throughput
HEAVY END LIGHT END
Rec. % Pur. % Rec. % Pur. %
CMS 13X L(STP) L-1h-1 CO 2 CO2 CH4 CH4 0 100 116.55 96.13 89.07 96.11 98.75 155.40 99.75 90.31 96.17 99.72 194.24 98.75 94.72 98.05 99.46 233.09 97.84 96.56 98.70 99.18 271.94 91.55 97.09 99.00 97.01 310.79 78.92 96.62 99.05 93.07 20 80 116.55 99.57 55.67 72.44 99.94 155.40 99.87 81.59 92.11 99.87 194.24 99.53 91.85 96.86 99.84 233.09 98.64 96.18 98.62 99.53 271.94 85.58 95.96 98.73 95.21 310.79 73.72 95.60 98.86 91.52 40 60 116.55 100.02 59.16 75.79 99.94 155.40 99.81 66.62 82.51 99.95 194.24 99.23 93.63 97.55 99.73 233.09 96.15 95.50 98.39 98.69 271.94 81.49 95.10 98.57 93.87 310.79 70.64 94.79 98.60 90.58 60 40 116.55 99.84 53.28 69.43 100.00 155.40 99.98 62.11 78.69 99.99 194.24 98.99 93.73 97.57 99.64 233.09 92.10 94.71 98.26 97.31 271.94 77.78 94.26 98.29 92.70 310.79 67.95 93.97 98.51 89.79 80 20 116.55 99.01 88.17 95.43 99.64 155.40 98.58 91.46 96.83 99.49 194.24 97.14 93.43 97.55 99.02 233.09 87.13 93.86 98.09 95.64 271.94 74.77 93.53 98.12 91.76 310.79 65.86 93.25 98.24 89.17 100 0 116.55 93.17 87.56 95.40 97.56 155.40 90.58 90.45 96.66 96.71 194.24 88.33 92.25 97.36 95.98 233.09 83.51 93.17 97.90 94.44 271.94 73.14 93.00 98.19 91.26 310.79 64.80 92.75 98.28 88.86
55
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Figure 2.2. Simulation results as % CH4 recovery vs. purity on light product at the periodic steady state for different layer combinations of beds and for different feed throughputs (Perfect negative approach applied on both adsorbents for mixed gas adsorption isotherms). Symbols are for different layer amounts of CMS (+ for 0 %, X for 20 %, ▲ for 40 %, ♦ for 60 %, ■ for 80 %, ● for 100 %) and the rest of the bed was filled with 13X. The volumetric feed throughput [L(STP) L-1h-1] is increasing (116.55, 155.40,
194.24, 233.09, 271.94, 310.79) from top left to bottom right for the same layer combination.
57
Figure 2.3. Simulation results as % CO2 recovery vs. purity on heavy product at the periodic steady state for different layer combinations of beds and for different feed
throughputs (Perfect negative approach applied on both adsorbents for mixed gas adsorption isotherms). Symbols are for different layer amounts of CMS (+ for 0 %, X for 20 %, ▲ for 40 %, ♦ for 60 %, ■ for 80 %, ● for 100 %) and the rest of the bed was filled with 13X. The volumetric feed throughput [L(STP) L-1h-1] is increasing (116.55, 155.40,
194.24, 233.09, 271.94, 310.79) from bottom right to top left for the same layer combination.
58
Figure 2.4. Total required energies for different layer combinations of beds and for different feed throughputs (Perfect negative approach on both CMS and 13X applied for mixed gas adsorption isotherms). Symbols are for different layer amounts of CMS (+ for 0 %, X for 20 %, ▲ for 40 %, ♦ for 60 %, ■ for 80 %, ● for 100 %) and the rest of the
59
Figure 2.5. Simulation results as % CH4 recovery vs. purity on light product at the periodic steady state for different layer combinations of beds and for different feed throughputs (Perfect negative approach on CMS and Perfect Positive on 13X applied for mixed gas adsorption isotherms). Symbols are for different layer amounts of CMS (+ for 0 %, X for 20 %, ▲ for 40 %, ♦ for 60 %, ■ for 80 %, ● for 100 %) and the rest of the bed was filled with 13X. The volumetric feed throughput [L(STP) L-1h-1] is increasing (116.55, 155.40, 194.24, 233.09, 271.94, 310.79) from top left to bottom right for the
60
Figure 2.6. Simulation results as % CO2 recovery vs. purity on heavy product at the periodic steady state for different layer combinations of beds and for different feed